2. Pure Mathematics 2

Parametric Curves — Quiz

Test your understanding of parametric curves with 5 practice questions.

Practice Questions

Question 1

For the parametric curve $x=t^2$, $y=t^3$, what is the value of the second derivative $\dfrac{d^2y}{dx^2}$ at $t=1$?

Question 2

Eliminate the parameter for the curve given by $x=2\sec t$ and $y=3\tan t$. What is the resulting Cartesian equation?

Question 3

For the cycloid defined by $x=r(t-\sin t)$, $y=r(1-\cos t)$, what is the arc length of one arch for $0\le t\le2\pi$?

Question 4

For the parametric equations $x=3t^2$, $y=2t^2$, what is the speed $v(t)=\sqrt{(dx/dt)^2+(dy/dt)^2}\$ at $t=1$?

Question 5

A cusp on a smooth parametric curve occurs at a parameter value $t=t_0$ if which condition holds?